There are only questions that finding the number of ideals in my book.
So I have a curious that how many each ring does have subrings.
How many number of the subring for given rings?
(Each of the below rings have an identity that $0=[0]_n $ for $mod n$ and unity $1=[1]_n $ for $mod n$
E.g. the ring $\mathbb Z_6 =\{0,1,2,3,4,5\}$ for $mod n$(unity is 1 and identity is 0)
- $\mathbb Z_6$
- $\mathbb Z_4$
- $\mathbb Z_6 \times \mathbb Z_4$
- $\mathbb Z_7$
P.s.) how many number of the subrings which is isomorphic with the ring $\mathbb Z_n$?